Damping of Bogoliubov Excitations in Optical Lattices

Details Damping of Bogoliubov Excitations in Optical Lattices Damping of Bogoliubov Excitations in Optical Lattices

2003-11-13

arxiv.org/abs/cond-mat/0311321v1

Physics

Condensed Matter

Soft Condensed Matter

4pages, 5figures, submitted to Phys. Rev. Lett

Scientific paper

10.1103/PhysRevA.70.023611

Extending recent work to finite temperatures, we calculate the Landau damping of a Bogoliubov excitation in an optical lattice, due to coupling to a thermal cloud of such excitations. For simplicity, we consider a 1D Bose-Hubbard model and restrict ourselves to the first energy band. For energy conservation to be satisfied, the excitations in the collision processes must exhibit ``anomalous dispersion'', analogous to phonons in superfluid $^4\rm{He}$. This leads to the disappearance of all damping processes when $U n^{\rm c 0}\ge 6t$, where $U$ is the on-site interaction, $t$ is the hopping matrix element and $n^{\rm c 0}(T)$ is the number of condensate atoms at a lattice site. This phenomenon also occurs in 2D and 3D optical lattices. The disappearance of Beliaev damping above a threshold wavevector is noted.

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